Two planes P1 and P2 pass through origin. Two lines L1 and L2 also passing through origin are such that L1 lies on P1 but not on P2, L2 lies on P2 but not on P1.
A,B< C are three points other than origin, then prove that the permutation [A',B',C'] of [A,B,C] exists such that
i) A lies on L1, B lies on P1 not L1, C does not lie on P1
ii) A' Lies on L2, B' lies on P2 not on L2, C' does not lie on P2
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1 Answers
1here 6 permutations are possible as A corresponds to one of A',B',C'
and B corresponds to one of remaining A',B',C' and C corresponds to third of A',B',C'
therefore A lies on L1, B lies on the line of intersection of P1and P2 and C lies on L2 on the plane of P2
therefore A' lies on L2=C
B' lies on the line of intersection of P1and P2=B
C' lies on L1 on the plane of P1=A
i.e permutation of [A'B'C']=[ABC]